Shadow Yukiko is harder in base P4. It doesn't have the weakness to Ice that it does in Golden (Though the minion is still weak to ice) and it has Mind Charge that it uses if it knocks down someone (See: Chie).
For General advice, Yu wants a persona that has ice and isn't weak to fire. You can get that with Persona fusion. Remember in Persona fusion in P4 the abilities are random but you can back out of the selection, unselect the personas your using for fusion and rechose them and it will reset what moves you inherit. I can't remember if there is a persona that's resistant to fire, but use that if there is. For the others, Yosuke is the only thing that can heal in this match unless Yu has a persona with Dia that isn't Pixie (Weak to fire). Other than that, use items. Chie is probably your best friends and worst enemy in this fight. She has Bufu but is weak to fire. Guard with her every now and again if you think the boss is gonna try something though there's no real tell unlike Shadow Yosuke. If she uses Mind Charge, guard with everyone.
The Minion resists wind but is weak to ice. It's main purpose is to be an annoyance until you kill it and then never come back once it dies once. It has 850HP. Uses Chie and Yu to kill it quick. As you said, it heals Yukiko which is the last thing you want. It also has Sukukaja which is also a nuisance.
Shadow Yukiko herself is Level 15, so another level or two wouldn't hurt. I think I was around level 12 when I did it though that was a long time ago. As I'm sure you know, her signature move "Burn to Ashes" hurts though it's pretty much just Magilao (Medium Fire to everyone). Guard with Chie often but not so often you aren't using her to do damage. When the prince is out, don't guard with Chie. Just kill it. Shivering Rondo, her other signature moves, only seems to affect those who are hit with Fear from the prince. Since it's not Golden, you don't have to worry about her inflicting it herself
All the info I got is from the Megami Tensei Wiki, which is a nice place if you want to know moves and stats of the bosses and enemies you face. The Prince's data is on the same page as well as a few more tips. Link Below:
Other than that, just don't give up, pack a few revival items if you can get them and heal often with items, Yu or Yosuke. If you can crit with a Physical move from Chie, great. That's a free All Out Attack. Just don't rely on them. Shadow Yukiko has around 1,000 HP in base 4, so it shouldn't take that long if you keep on top of things.
(edited by Gin)